A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/4#. If side C has a length of #1 # and the angle between sides B and C is #( 3 pi)/8#, what are the lengths of sides A and B?

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Answer 1 · 2018-06-04T12:01:55

Length of sides #A and B# are #1.31# unit each.

Angle between sides # A and B# is # /_c= pi/4=180/4=45^0#

Angle between sides # B and C# is # /_a= (3pi)/8=540/8=67.5^0 #

Angle between sides # C and A# is

# /_b= 180-(45+67.5)=67.5^0 # . This is an isosceles triangle.

The sine rule states if #A, B and C# are the lengths of the sides

and opposite angles are #a, b and c# in a triangle, then:

#A/sinA = B/sinb=C/sinc ; C=1 :. B/sin b=C/sin c# or

#B/sin 67.5=1/sin 45 or B= 1* (sin 67.5/sin 45) ~~ 1.31 (2dp) #

Similarly #A/sina=C/sinc # or

#A/sin 67.5=1/sin 45 or A= 1* (sin67.5/sin 45) ~~ 1.31 (2dp) #

Length of sides #A and B# are #1.31# unit each [Ans]